document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=61668>Question 61668</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The hypotenuse of a right triangle is 6 inches longer than the shortest side and 3 inches longer than the remaining side. Find the dimensions of the triangle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #42439 by </B><A HREF=/tutors/aboutme.mpl?userid=joyofmath><B>joyofmath(189)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=joyofmath><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=42439\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The hypotenuse of a right triangle is 6 inches longer than the shortest side and 3 inches longer than the remaining side. Find the dimensions of the triangle\r<BR>\n" );
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document.write( "Let S be the short side of the triangle. <BR>\n" );
document.write( "Then S+6 is the hypotenuse.<BR>\n" );
document.write( "And, the remaining side is S+3 because it's 3 inches shorter than the hypotenuse.\r<BR>\n" );
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document.write( "So, using the Pythagorean Theorem: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E2%2B%28S%2B3%29%5E2+=+%28S%2B6%29%5E2 ALIGN=MIDDLE  ALT=\"S%5E2%2B%28S%2B3%29%5E2+=+%28S%2B6%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Square everything and we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E2+%2B+S%5E2%2B6S%2B9+=+S%5E2%2B12S%2B36 ALIGN=MIDDLE  ALT=\"S%5E2+%2B+S%5E2%2B6S%2B9+=+S%5E2%2B12S%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2S%5E2%2B6S%2B9+=+S%5E2%2B12S%2B36 ALIGN=MIDDLE  ALT=\"2S%5E2%2B6S%2B9+=+S%5E2%2B12S%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E2 ALIGN=MIDDLE  ALT=\"S%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E2%2B6S%2B9+=+12S%2B36 ALIGN=MIDDLE  ALT=\"S%5E2%2B6S%2B9+=+12S%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Subtract 12S from both sides: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E2-6S%2B9+=+36 ALIGN=MIDDLE  ALT=\"S%5E2-6S%2B9+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Subtract 36 from both sides: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E2-6S-27+=+0 ALIGN=MIDDLE  ALT=\"S%5E2-6S-27+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "This factors into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28S-9%29%28S%2B3%29+=+0+ ALIGN=MIDDLE  ALT=\"%28S-9%29%28S%2B3%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=9 ALIGN=MIDDLE  ALT=\"S=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=-3 ALIGN=MIDDLE  ALT=\"S=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. But, S can't be negative, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=9 ALIGN=MIDDLE  ALT=\"S=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Verify that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=9 ALIGN=MIDDLE  ALT=\"S=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is correct.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E2%2B%28S%2B3%29%5E2+=+9%5E2+%2B+12%5E12+=+81+%2B+144+=+225 ALIGN=MIDDLE  ALT=\"S%5E2%2B%28S%2B3%29%5E2+=+9%5E2+%2B+12%5E12+=+81+%2B+144+=+225\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is indeed <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%5E2 ALIGN=MIDDLE  ALT=\"15%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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